The concept and properties of quasi-rigid $C_{0}$-semigroups

In this paper, quasi-rigid $C_{0}$-semigroups are introduced and their properties are investigated.Also, some sufficient conditions for quasi-rigidity are stated.It is proved that quasi-rigid $C_{0}$-semigroups are recurrent.It is stated that if a $C_{0}$-semigroup contains a quasi-rigid operator, then it is quasi-rigid.The concept of topologically

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